We demonstrate generation of pulses with up to $4\mu \mathrm{J}$ energy at $1\mathrm{MHz}$ repetition rate through nonlinear chirped-pulse amplification in an entirely fiber-integrated amplifier, seeded by a fiber oscillator. The peak power and the estimated nonlinear phase shift of the amplified pulses are as much as $57\mathrm{kW}$ and $22\pi$ , respectively. The shortest compressed pulse duration of $140\mathrm{fs}$ is obtained for $3.1\mu \mathrm{J}$ of uncompressed amplifier output energy at $18\pi$ of nonlinear phase shift. At $4\mu \mathrm{J}$ of energy, the nonlinear phase shift is $22\pi$ and compression leads to $170\text{-}\mathrm{fs}$ -long pulses. Numerical simulations are utilized to model the experiments and identify the limitations. Amplification is ultimately limited by the onset of Raman amplification of the longer edge of the spectrum with an uncompressible phase profile.